TY - JOUR

T1 - Rota–Baxter operators on groups

AU - Bardakov, Valeriy G.

AU - Gubarev, Vsevolod

N1 - The authors are grateful to participants of the seminar “Évariste Galois” at Novosibirsk State University for fruitful discussions. The second author is grateful to Alexey Staroletov for helpful discussions. The authors are also grateful to the anonymous reviewer for useful remarks. The second author is supported by RAS Fundamental Research Program, Project FWNF-2022-0002. The first author is supported by Ministry of Science and Higher Education of Russia (Agreement No. 075-02-2022-884). The results of §3, §5, §7 and §8 are supported by Ministry of Science and Higher Education of Russia (Agreement No. 075-02-2022-884), while the results of §4, §6, §9, and §10 are supported by RAS Fundamental Research Program, Project FWNF-2022-0002. Публикация для корректировки.

PY - 2023/6

Y1 - 2023/6

N2 - The theory of Rota–Baxter operators on rings and algebras has been developed since 1960. In 2020, the notion of Rota–Baxter operator on a group was defined. Further, it was proved that one may define a skew left brace on any group endowed with a Rota–Baxter operator. Thus, a group endowed with a Rota–Baxter operator gives rise to a set-theoretical solution to the Yang–Baxter equation. We provide some general constructions of Rota–Baxter operators on a group. Given a map on a group, we study its extensions to a Rota–Baxter operator. We state the connection between Rota–Baxter operators on a group and Rota–Baxter operators on an associated Lie ring. We describe Rota–Baxter operators on sporadic simple groups.

AB - The theory of Rota–Baxter operators on rings and algebras has been developed since 1960. In 2020, the notion of Rota–Baxter operator on a group was defined. Further, it was proved that one may define a skew left brace on any group endowed with a Rota–Baxter operator. Thus, a group endowed with a Rota–Baxter operator gives rise to a set-theoretical solution to the Yang–Baxter equation. We provide some general constructions of Rota–Baxter operators on a group. Given a map on a group, we study its extensions to a Rota–Baxter operator. We state the connection between Rota–Baxter operators on a group and Rota–Baxter operators on an associated Lie ring. We describe Rota–Baxter operators on sporadic simple groups.

KW - Rota–Baxter group

KW - Rota–Baxter operator

KW - factorization

KW - simple group

KW - sporadic group

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85149265321&origin=inward&txGid=52e805d099521ad506f77995ea46da57

UR - https://www.mendeley.com/catalogue/9e7c6c39-875e-384f-972a-3162986bbdfc/

U2 - 10.1007/s12044-023-00723-9

DO - 10.1007/s12044-023-00723-9

M3 - Article

VL - 133

JO - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

JF - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

SN - 0253-4142

IS - 1

M1 - 4

ER -